for the train schedules have a look at the site that kileysmom suggested: www.sbb.ch.
there is a TGV train that goes directly from Basel to Paris and leaves from (normally) platform 5 from the SBB main station at 08:02, 10:55 15:02 and 19:02 hours. You must have a reservation for this train.
There are more trains of course between Basel and Paris, with one change in Strasbourg (of which you might want to profit and spent a couple of hours there-it is a very beautiful city)for whch I do not kno wif you need reservations beforehand.
I think the best thing for you to do is to plan when you want to go and buy the tickets and reservations online (from the site above) This will save time queing at the station.Plus you can profit from the offers.
browse a bit for the prices, because there are good offers to be found. The one that is permanent is the piccolisimo and Piccolo:
the distance between your port of arrival (Dreiländereck) and the railroad station is about 7 kilometres and there are trams but it will be more easy to get a taxi. Do not worry about that, taxi drivers are honest in Switzerland. It will cost you about 25 to 30 swiss francs (22 to 27 usd). Make clear that you want The SBB Railroad Station and not the Badischer Bahnhof.
I hope this helps a bit. Pls ask if you have more questions
PS: hallo back at you kileysmom. Sorry for not being in contact or in the forum- I am a bit under the weather.